No chemical graph on more than two vertices is nuciferous

Irene Sciriha, Alexander Farrugia

Abstract


A simple graph is nuciferous if its 0–1 adjacency matrix is nonsingular and if its inverse has zero entries on its main diagonal and a non–zero entry at each off–diagonal position. A nuciferous graph is a molecular graph that represents an ipso omni–insulating but distinct omni–conducting molecule. It has been conjectured in 2012 that only K2, the complete graph on two vertices, is nuciferous. We show that this conjecture is true for chemical graphs, that is, graphs whose vertex degree is at most three.


Keywords


Nuficerous graph, chemical graph, NSSD, non-singular graph, molecular conductivity

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DOI: https://doi.org/10.26493/1855-3974.1030.9d9

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications